1. Field of the Invention
The present invention relates to a position control system which permits accurate position control of a numerical-controlled machine tool.
2. Description of the Prior Art
A position control system that has heretofore been proposed for numerical-controlled machine tools, as shown in FIG. 1, employs a semi-closed loop type servomechanism. With this conventional system, for example, the rotational angle of a motor shaft is detected by a position detector DET1, such as a resolver or the like, and the detected position information x is negatively fed back to a position control section NC of a numerical control unit, wherein it is provided via an A-D converter AD to an adder A. In the adder A, a difference is detected between position information x and commanded position information r to obtain a position deviation e. The position deviation e is applied via a gain setting circuit GC and a D-A converter DA to a velocity amplifier AMP, by which a motor M is driven in such a manner as to reduce the position deviation e to zero, and the motor rotating a reduction gear GEAR and a ball screw V controlling the position of a moving table MC. FIG. 2 shows an example of a block diagram corresponding to FIG. 1. In FIG. 2, reference character K indicates the gain of the gain setting circuit GC; G.sub.1 (s) designates the transfer function of a velocity control section composed of the velocity amplifier AMP; G.sub.2 (s) identifies the transfer function of the motor shaft M; and .omega..sub.v denotes the break point angular frequency of the transfer function of the velocity control section. As is evident from FIG. 2, since the mechanical system is placed outside the closed loop system, the semi-closed loop type servomechanism allows easy maintenance of the closed loop system stability, and accordingly it is adopted in various machine tools. A discussion follows of the movement x of the motor shaft in the case where the ramp input specified in equation (1) is applied as the commanded position information r to a numerical-controlled machine tool. EQU r=F.times.t (1)
where F is a feed rate and t is time. The transfer function G(s) of the abovesaid closed loop is given as follows: ##EQU1## Letting the Laplace transformation of the input r be represented by R(s), a deviation E(s) on its desired value R(s) becomes as follows: ##EQU2## Accordingly, the steady-state deviation e (t.fwdarw..infin.) becomes as follows: ##EQU3## The movement of the motor shaft, and accordingly the movement of the moving table MC, in its steady-state, has a certain amount of time lag which is proportional to the feed rate and inversely proportional to the gain K. This delay has a direct influence on the actual cutting accuracy. For example, when cutting a workpiece by straight cutting into the configuration indicated by reference numeral 1 of FIG. 3, the actual locus of movement of a tool causes a cut as indicated by reference numeral 2; namely, the corner of the work is rounded in proportion to the delay. When making a circular cut, the locus of movement 2 of the tool deviates from a true circle 3, as illustrated in FIG. 4. When the tool is suddenly stopped while running at a constant speed, the actual tool movement overruns by the delay. Consequently, the overrun poses a problem when stopping the cutting operation by stepping on a stroke switch of the machine tool. As is apparent from equation (4), an increase in the gain K decreases the delay, however, there is an upper limit to the magnitude of the gain K which can be used and still remain in a stable region and it is difficult to correct the delay in that upper range.
Various problem resulting from such steady-state deviation are encountered not only in the aforesaid semi-closed loop type numerical-controlled machine tool but also in a closed loop type numerical-controlled machine tool such, for example, as shown in FIG. 5. In the closed loop type a position detector DET2, such as an inductive detector or the like, is mounted on a moving part of the machine tool to be ultimately controlled, for example, the moving table. The detected position information is negatively fed back so that it may coincide with the commanded position information r. Accordingly, it has been desired to solve the above outlined problems.